Add fractions with unlike denominators?
I'm a little rusty with fractions, have a quiz coming up for an entrance exam. When adding fractions with unlike denominators, do you always just multiply the denominators by each other? The rule is you are supposed to multiply them by the LCD and it seems like I almost always see myself just end up multiplying...
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answers:
Jeffrey K say: That will always work but your answer may not be in lowest terms.
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electron1 say: 7 and 5 do not have a common factor. For this reason, the lowest common denominator is the product of these two numbers. 35

2/7 * 5/5 = 10/35
3/5 * 7/7 = 21/35

2/7 + 3/5 = 10/35 + 21/35 = 31/35

Let’s add ¾ and 5/12. 12 is 3 * 4. So the lowest common denominator is 12. So we only need to convert ¾ to x/12

¾ * 3/3 = 9/12
9/12 + 5/12 = 15/12

Divide the numerator and denominator by 3.

15/12 = 4/3 = 1 ⅓

I hope this is helpful for you.
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Como say: 2/7 + 3/5

10 + 21
------------------
35

31
-----
35
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david say: Multiply each by some factor to create the LOWEST common denominator.

This involves factoring each denominator and then ignoring the common factors. ,,, ex 7/10 + 8/15
10 = 2x5 and 15 = 3x5 ... common factor is 5
multiply the first fraction by 3/3 to create 30 for the denom.
multiply the 2nd fraction by 2/2 to create 30 for the denom.
----- do not multiply anything by the common factor, 5.

3/3 X 7/10 = 21/30
2/2 X 8/15 = 16/30 ... now they have a common denom. of 30

the problem becomes
21/30 + 16/30 = 37/30 ... change into mixed number if needed
= 1 7/30 ...
so, no do not always multiply both denom. together.
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Puzzling say: In order to add fractions, you must get a common denominator and preferably the lowest common denominator.

For example:
1/4 + 1/6

The lowest common denominator is 12.

1/4 --> 3/12
1/6 --> 2/12

Adding:
3/12 + 2/12
= 5/12

That's the preferred method, but you may also just multiply the two denominators.
4 × 6 = 24

1/4 = 6/24
1/6 = 4/24

Adding:
6/24 + 4/24
= 10/24

And now you should reduce the fraction to lowest terms:
10/24 = 5/12

So if you figure out the lowest common denominator, you can save some reducing, but either way works.

As for 2/7 + 3/5, because the denominators have no factors in common, just multiplying gets you the lowest common denominator anyway.
5 × 7 = 35

2/7 --> 10/35
3/5 --> 21/35

Sum:
31/35
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llaffer say: "Do you always just multiply the denominators by each other"?

I would say no, but you can if you want but you will always have to reduce at the end.

Using your example, you have to:

2/7 + 3/5

LCD here is 35, so:

10/35 + 21/35
31/35

But in cases where the denominators have a common factor, such as:

1/2 + 5/6

The LCD here is 6. But nothing is stopping you from using a denominator of 12, you will just have to reduce at the end. I'll do this twice, once using LCD and the other using the product:

3/6 + 5/6 and 6/12 + 10/12
8/6 and 16/12
4/3 and 4/3

Both required different reducing to get to the final answer, but the answers are the same, so ultimately you can use whatever common denominator you wish. The workbooks usually "want" you to use the LCD, but it isn't required if you properly reduce at the end.
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